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Recursive contracts in non-convex environments

Author

Listed:
  • Chengfeng Shen
  • Felix Kubler
  • Zhennan Zhou

Abstract

In this paper we examine non-convex dynamic optimization problems with forward looking constraints. We prove that the recursive multiplier formulation in \cite{marcet2019recursive} gives the optimal value if one assumes that the planner has access to a public randomization device and forward looking constraints only have to hold in expectations. Whether one formulates the functional equation as a sup-inf problem or as an inf-sup problem is essential for the timing of the optimal lottery and for determining which constraints have to hold in expectations. We discuss for which economic problems the use of lotteries can be considered a reasonable assumption. We provide a general method to recover the optimal policy from a solution of the functional equation. As an application of our results, we consider the Ramsey problem of optimal government policy and give examples where lotteries are essential for the optimal solution.

Suggested Citation

  • Chengfeng Shen & Felix Kubler & Zhennan Zhou, 2025. "Recursive contracts in non-convex environments," Papers 2511.20303, arXiv.org.
    • Handle: RePEc:arx:papers:2511.20303
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    References listed on IDEAS

    as
    1. Gaetano Bloise & Paolo Siconolfi, 2022. "A Negishi Approach to Recursive Contracts," Econometrica, Econometric Society, vol. 90(6), pages 2821-2855, November.
    2. Thomas Cooley & Ramon Marimon & Vincenzo Quadrini, 2004. "Aggregate Consequences of Limited Contract Enforceability," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 817-847, August.
    3. Edward Simpson Prescott, 1999. "A primer on moral-hazard models," Economic Quarterly, Federal Reserve Bank of Richmond, issue Win, pages 47-78.
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